Aerospace and Electronic Systems Magazine October 2017 - 17

Menon et al.
relation between the frequency shift and the substrate bending
angle is:
Δf
fθ − f 0
=
Δθ sin −1 ((2Δy ) / l )

(2)

Δf
, fθ and f0 are obtained from experimental data. AdditionΔθ
ally, S11 is defined as:

where

S11 =

Er 1
Ei1

(3)

where, Ei1 is the injected energy and Er1 is the reflected energy.
Given the output impedance Z0 and the load impedance ZL of the
material being tested, S11 can also equivalently be expressed as follows [18]:
S11 =

Z L − Z0
Z L + Z0

(4)

The value of ZL changes with the resonant frequency fθ [18], which
itself is a function of the bending angle of the substrate according
to (2). Thus, a change in the bending angle causes a shift in the
resonant frequency according to (2), which leads to a change in the
load impedance, and subsequently a change in the S11 parameter,
according to (4).

Figure 5.

SansEC mounted plate on a MTS machine.

TESTING OF BENDING MEASUREMENTS BY SANSEC
SENSOR
A square polycarbonate substrate with a SansEC sensor adhered to the surface was constrained along one edge, as shown
in Figure 5. The opposite edge of the substrate was subjected to
bending on a vertical plane, using an MTS mechanical testing
system. Two tests were conducted: a static deflection test followed by a dynamic deflection test. In each of these tests, the
substrate was deflected over a range of 0 to 1 inch. During the
static deflection test, the substrate was deflected to a specified
distance and then held in position while the SansEC data was collected. During the dynamic experiment, the MTS machine was
programmed to move from 0 to 1 inch at a rate of 15 in/min for
several cycles.
Figure 6 shows a time history of the plate's dynamic deflection
(grey curve), with time on the bottom horizontal axis and deflection on the right vertical axis. Also shown in the figure are the corresponding sensor sensing S11 measurements (red curve) collected
with a SARK network analyzer, and these are shown as a function of frequency, with frequency on the top horizontal axis and
S11 amplitude on the left vertical axis. The frequency-dependent
development of the dynamic curve is synchronized in time with
the plate's deflection cycle. This synchronization is performed as
follows: The time taken by the SARK analyzer to collect each data
point is a constant. Thus, for a given frequency range and a given
number of data points to be collected over that frequency range,
one can determine the total time taken by the SARK analyzer to
complete the sweep over that frequency range.
OCTOBER 2017

Figure 6.

Dynamic SansEC curve (red), true plate deflection (grey), and grid
curves (black).

For the plot shown in Figure 6, 1,000 data points were collected by the SARK analyzer as it swept over the frequency range
of 8.2 MHz to 8.6 MHz. Thus, for instance, at a time of 4.7 sec,
the plate deflection is 1 inch, and the S11 amplitude is about -3 dB,
while at a time of 8.7 sec, the plate deflection is 0 inch, and the
S11 amplitude is about -10 dB. In addition, Figure 6 also shows
a series of S11 black curves, and these curves correspond to static

IEEE A&E SYSTEMS MAGAZINE

17



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